Related papers: Conditionally flat functors on spaces and groups

We construct an $(\infty,1)$-functor that takes each smooth $G$-manifold with corners $M$ to the space of equivariant smooth $h$-cobordisms ${\mathcal H}_{\mathrm{Diff}}(M)$. We also give a stable analogue ${\mathcal H}^{\mathcal…

Let $\bold G$ be a reductive algebraic group defined over $\Q$, and let $\Gamma$ be an arithmetic subgroup of $\bold G(\Q)$. Let $X$ be the symmetric space for $\bold G(\R)$, and assume $X$ is contractible. Then the cohomology (mod torsion)…

We study various operator homological properties of the Fourier algebra $A(G)$ of a locally compact group $G$. Establishing the converse of two results of Ruan and Xu, we show that $A(G)$ is relatively operator 1-projective if and only if…

A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…

In this article, we give a representation of bounded complex linear operators which preserve idempotent elements on the Fourier algebra of a locally compact group. When such an operator is moreover positive or contractive, we show that the…

We study several structure aspects of functor categories from a small additive category to a module category, in particular the category F(A,K) of functors from finitely generated free modules over a commutative ring A to vector spaces over…

The behavior of factorization properties in various ring extensions is a central theme in commutative algebra. Classically, the UFDs are (completely) integrally closed and tend to behave well in standard ring extensions, with the notable…

It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…

Cosmological $\alpha$-attractors are observationally favored due to the asymptotic flatness of the potential. Since its flatness induces the negative pressure even after inflation, the coherent oscillation of the inflaton field could…

We present a new and very short proof of the fact that, for positive $C_0$-semigroups on spaces of continuous functions, the spectral and the growth bound coincide. Our argument, inspired by an idea of Vogt, makes the role of the underlying…

We study the following question: under what conditions extension of one residually nilpotent group by another residually nilpotent group is residually nilpotent? We prove some sufficient conditions under which this extension is residually…

Let $R$ be a commutative unital ring and $a\in R.$ We introduce and study properties of a functor $a\Gamma_{a}(-),$ called the locally nilradical on the category of $R$-modules. $a\Gamma_{a}(-)$ is a generalisation of both the torsion…

Let X=Gamma\G/K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has Q-rank 1, we construct Gamma-equivariant deformation retractions of D=G/K onto a set D_0. We prove that D_0 is a spine, having…

In this paper we discuss extensions of the canonical quantization procedure in quantum field theories. We focus specifically on S-matrix representation as a T-exponent. This extension involves flat bundles on certain infinite dimensional…

We construct a flat model structure on the category $_{\mathcal{Q},R}{\mathsf{Mod}}$ of additive functors from a small preadditive category $\mathcal{Q}$ satisfying certain conditions to the module category $_{R}{\mathsf{Mod}}$ over an…

We prove the following criterion for the pro-representability of the deformation cohomology of a commutative formal Lie group. Let f be a flat and separated morphism between noetherian schemes. Assume that the target of f is flat over the…

We revise the construction of the augmented Cuntz semigroup functor used by the first author to classify inductive limits of 1-dimensional noncommutative CW complexes. The original construction has good functorial properties when restricted…

Let $M$ be a connected 1-manifold, i.e., $M = \R \cong (0, 1), [0, 1), [0, 1]$, or $S^1$, and let $\Homeo_+(M)$ (resp. $\Diff_+^1(M)$) be the group of orientation-preserving homeomorphisms (resp. $C^1$ diffeomorphisms) of $M$. It is a…

Let $\Gamma$ be a finite dimensional Lie group and consider the smooth double loop group, i.e. the Fr\'echet Lie group of smooth maps from the 2-torus to $\Gamma$. For a finite dimensional Hilbert space V, let H denote the Hilbert space of…

For any ring $A$ and a small, preadditive, Hom-finite, and locally bounded category $Q$ that has a Serre functor and satisfies the (strong) retraction property, we show that the category of additive functors from $Q$ to the category of…